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If I have time series data that non-normally distributed and non-linear what the suitable statistical method should I use for testing stationarity and for estimation?

If I have time series data that non-normally distributed and non-linear what the suitable statistical method should I use for testing stationarity and for estimation?

The second question is the Augmented Dickey-Fuller (ADF) unit root test could use to test stationarity in this situation?

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